Tri-city has three railroad tracks that run north to south or east to west across the city. The 

     railroad tracks are represented by the asymptotes of a function fx=(2x^2-2x-5)/x^2-2x-8. The roads 

     travel along the path of the function. The railroad tracks and roads intersect at one location. 

     Determine the coordinates of the intersection.  

 

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The two north-south tracks are x=4 and x=-2 because these are the zeroes of x²-2x-8=(x-4)(x+2) in the denominator. The east-west track is y=2, the horizontal asymptote, which intersects the other two tracks at (4,2) and (-2,2).

One road is intersected by the track:

2=(2x²-2x-5)/(x²-2x-8),

2x²-4x-16=2x²-2x-5,

-4x-16=-2x-5,

-11=2x, so x=-11/2 and the intersection is (-11/2,2).

 

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